Let f be a function defined on `[a, b]` such that `f'(x)>0` for all `x in (a,b)`. Then prove that f is an increasing function on `(a, b)`.

Let f be an even function and f'(x) exists, then f'(0) is

Let the function f:9R to 9R be defined by f(x)=2x+sin for all x in 9R . Then f(x) is

Let A be the set of all 50 students of class XII in a school. Let f: A rarr N be the function defined by : f (x) = Roll number of the student x. Prove that 'f' is one-one but not onto.

Let f(x) be polynomial function of degree 2 such that f(x)gt0 for all x in R. If g(x)=f(x)+f'(x)+f''(x) for all x, then

Let N rarr N be defined by f (x) = 3x. Show that f is not an onto function.

Let f : X rarr Y be a function. Define a relation R in X given by R = {(a, b): f (a) = f (b)} Examine whether R is an equivalence relation or not.

Let f : R rarr R be the functions defined by f(X) = x^3 + 5 , then f^-1 (x) is

A function f: R rarr R be defined by f(x) = 5x+6. prove that f is one-one and onto.